Q-Q plots with con dence for testing Weibull and exponential distributions

Abstract

One of the basic graphical methods for assessing the validity of a distributional assumption is the Q-Q plot which compares quantiles of asample against the quantiles of the distribution. In this paper, we focuson how a Q-Q plot can be augmented by intervals for all the points sothat, if the population distribution is Weibull or exponential then allthe points should fall inside the corresponding intervals simultaneouslywith probability 1 - ?. These simultaneous 1 - ? probability intervalsprovide therefore an objective mean to judge whether the plotted pointsfall close to the straight line: the plotted points fall close to the straightline if and only if all the points fall within the corresponding intervals.The powers of ve Q-Q plot based graphical tests and the most popularnon-graphical Anderson-Darling and Cramér-von-Mises tests are compared by simulation. Based on this power study, the tests that havebetter powers are identi ed and recommendations are given on whichgraphical tests should be used in what circumstances. Examples areprovided to illustrate the methods